Properties

Conductor 3009
Order 464
Real No
Primitive No
Parity Even
Orbit Label 6018.bn

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(6018)
sage: chi = H[5]
pari: [g,chi] = znchar(Mod(5,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 3009
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 464
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = No
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 6018.bn
Orbit index = 40

Galois orbit

sage: chi.sage_character().galois_orbit()
pari: order = charorder(g,chi)
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

\(\chi_{6018}(5,\cdot)\) \(\chi_{6018}(29,\cdot)\) \(\chi_{6018}(41,\cdot)\) \(\chi_{6018}(71,\cdot)\) \(\chi_{6018}(95,\cdot)\) \(\chi_{6018}(107,\cdot)\) \(\chi_{6018}(125,\cdot)\) \(\chi_{6018}(143,\cdot)\) \(\chi_{6018}(167,\cdot)\) \(\chi_{6018}(197,\cdot)\) \(\chi_{6018}(245,\cdot)\) \(\chi_{6018}(299,\cdot)\) \(\chi_{6018}(311,\cdot)\) \(\chi_{6018}(317,\cdot)\) \(\chi_{6018}(371,\cdot)\) \(\chi_{6018}(449,\cdot)\) \(\chi_{6018}(479,\cdot)\) \(\chi_{6018}(521,\cdot)\) \(\chi_{6018}(551,\cdot)\) \(\chi_{6018}(605,\cdot)\) \(\chi_{6018}(617,\cdot)\) \(\chi_{6018}(635,\cdot)\) \(\chi_{6018}(641,\cdot)\) \(\chi_{6018}(653,\cdot)\) \(\chi_{6018}(677,\cdot)\) \(\chi_{6018}(725,\cdot)\) \(\chi_{6018}(737,\cdot)\) \(\chi_{6018}(743,\cdot)\) \(\chi_{6018}(779,\cdot)\) \(\chi_{6018}(845,\cdot)\) ...

Inducing primitive character

\(\chi_{3009}(5,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{3}{29}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{317}{464}\right)\)\(e\left(\frac{139}{464}\right)\)\(e\left(\frac{127}{464}\right)\)\(e\left(\frac{105}{116}\right)\)\(e\left(\frac{71}{232}\right)\)\(e\left(\frac{343}{464}\right)\)\(e\left(\frac{85}{232}\right)\)\(e\left(\frac{213}{464}\right)\)\(e\left(\frac{409}{464}\right)\)\(e\left(\frac{57}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{464})\)